Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

Simplified skin-effect formulation for power transmission lines

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

The single-phase induction motor:a critical appraisal of the rotating-field and cross-field theories with particular reference to skin effect

The purpose of this thesis is twofold: to examine the validity of the rotating-field and cross-field theories of the single-phase induction motor when applied to a cage rotor machine; and to examine the extent to which skin effect is likely to modify the characteristics of a cage rotor machine. A mathematical analysis is presented for a single-phase induction motor in which the rotor parameters are modified by skin effect. Although this is based on the usual type of ideal machine, a new form of model rotor allows approximations for skin effect phenomena to be included as an integral part of the analysis. Performance equations appropriate to the rotating-field and cross-field theories are deduced, and the corresponding explanations for the steady-state mode of operation are critically examined. The evaluation of the winding currents and developed torque is simplified by the introduction of new dimensionless factors which are functions of the resistance/reactance ratios of the rotor and the speed. Tables of the factors are included for selected numerical values of the parameter ratios, and these are used to deduce typical operating characteristics for both cage and wound rotor machines. It is shown that a qualitative explanation of the mode of operation of a cage rotor machine is obtained from either theory; but the operating characteristics must be deduced from the performance equations of the rotating-field theory, because of the restrictions on the values of the rotor parameters imposed by skin effect.

Effect of oxytocin on transepithelial transport of water and Na+ in distinct ventral regions of frog skin (Rana catesbeiana)

Thoracic, abdominal, and pelvic fragments of ventral skin of Rana catesbeiana were analysed regarding the effect of oxytocin on: (1) transepithelial water transport; (2) short-circuit current, (3) skin conductance and electrical potential difference; (4) Na+ conductance, the electromotive force of the Nat transport mechanism, and shunt conductance; (5) short-circuit current responses to fast Na+ by K+ replacement in the outer compartment, and (6) epithelial microstructure. Unstimulated water and Na+ permeabilities were low along the ventral skin. Hydrosmotic and natriferic responses to oxytocin increased from thorax to pelvis, Unstimulated Na+ conductance was greater in pelvis than in abdomen, the other electrical parameters being essentially similar in both skin fragments. Contribution of shunt conductance to total skin conductance was higher in abdominal than in pelvic skin. Oxytocin-induced increases of total skin conductance, Na+ conductance, and shunt conductance in pelvis were significantly larger than in abdomen, An oscillatory behaviour of the short-circuit current was observed only in oxytocin-treated pelvic skins. Decrease of epithelial thickness and increase of mitochondria-rich cell number were observed from thorax to pelvis, Oxytocin-induced increases of interspaces were more conspicuous in pelvis and abdomen than in thorax.

Electrical skin phenomena: a fractional calculus analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A reprocessing for climate of sea surface temperature from the Along-Track Scanning Radiometers: initial validation, accounting for skin and diurnal variability

An initial validation of the Along Track Scanning Radiometer (ATSR) Reprocessing for Climate (ARC) retrievals of sea surface temperature (SST) is presented. ATSR-2 and Advanced ATSR (AATSR) SST estimates are compared to drifting buoy and moored buoy observations over the period 1995 to 2008. The primary ATSR estimates are of skin SST, whereas buoys measure SST below the surface. Adjustment is therefore made for the skin effect, for diurnal stratification and for differences in buoy–satellite observation time. With such adjustments, satellite-in situ differences are consistent between day and night within ~ 0.01 K. Satellite-in situ differences are correlated with differences in observation time, because of the diurnal warming and cooling of the ocean. The data are used to verify the average behaviour of physical and empirical models of the warming/cooling rates. Systematic differences between adjusted AATSR and in-situ SSTs against latitude, total column water vapour (TCWV), and wind speed are less than 0.1 K, for all except the most extreme cases (TCWV < 5 kg m–2, TCWV > 60 kg m–2). For all types of retrieval except the nadir-only two-channel (N2), regional biases are less than 0.1 K for 80% of the ocean. Global comparison against drifting buoys shows night time dual-view two-channel (D2) SSTs are warm by 0.06 ± 0.23 K and dual-view three-channel (D3) SSTs are warm by 0.06 ± 0.21 K (day-time D2: 0.07 ± 0.23 K). Nadir-only results are N2: 0.03 ± 0.33 K and N3: 0.03 ± 0.19 K showing the improved inter-algorithm consistency to ~ 0.02 K. This represents a marked improvement from the existing operational retrieval algorithms for which inter-algorithm inconsistency is > 0.5 K. Comparison against tropical moored buoys, which are more accurate than drifting buoys, gives lower error estimates (N3: 0.02 ± 0.13 K, D2: 0.03 ± 0.18 K). Comparable results are obtained for ATSR-2, except that the ATSR-2 SSTs are around 0.1 K warm compared to AATSR

Fractional order electromagnetics

The Maxwell equations constitute a formalism for the development of models describing electromagnetic phenomena. The four Maxwell laws have been adopted successfully in many applications and involve only the integer order differential calculus. Recently, a closer look for the cases of transmission lines, electrical motors and transformers, that reveal the so-called skin effect, motivated a new perspective towards the replacement of classical models by fractional-order mathematical descriptions. Bearing these facts in mind this paper addresses the concept of static fractional electric potential. The fractional potential was suggested some years ago. However, the idea was not fully explored and practical methods of implementation were not proposed. In this line of thought, this paper develops a new approximation algorithm for establishing the fractional order electrical potential and analyzes its characteristics.

Virranahto ja jänniterasitukset taajuusmuuttajakäytöissä

Nykyiset IGB-transistorit voivat tuottaa jopa 30 ns nousureunoja, jolloin jänniterasitus jakautuu hyvin epätasaisesti käämien ja kierrosten kesken. Tämä ja eristeissä esiintyvät ilmataskut asettavat käämikierrosten välisten eristeiden jännitekestävyyden koetukselle, ja aiheuttavat riskin osittaispurkaukselle. Urassa hajavuon epätasaisen jakauman aiheuttama virranahto on yleensä ollut esillä suurissa koneissa, jotka toimivat 50 Hz:llä. Nykyään taajuusmuuttajien soveltaminen on mahdollistanut nimellistaajuudeltaan satojen hertsien suurnopeuskoneiden käämitysten valmistamisen pyörölangasta, jolloin virranahto tulee merkittäväksi, koska kierroksia on muutama urassa. Työssä mitattiin jännitteen jakautumista 3.5 MW:n tuulivoimageneraattorin segmentissä käyttäen käämitysten syöttöön erilaisia jännitteen nousuaikoja, ja pyrittiin arvioimaan onko kyseinen kone vaarassa kokea osittaispurkauksia elinikänsä aikana. Työssä on myös käsitelty virranahtoa käyttäen finiittielementtimenetelmää simuloimaan ja vertaamaan erilaisia tilanteita käämitystavoissa pyörölankakoneessa. Tämä on myös osittain sovellettavissa muotokuparilla käämittyihin koneisiin. Käämivyyhdin vyyhdenpään alueella tehdyn johdinnipun 180 asteen kierron vaikutusta simuloitiin ja sen aiheuttamaa parannusta varmennettiin käytännön mittauksilla.

Identification of Some Additional Loss Components in High-Power Low-Voltage Permanent Magnet Generators

Permanent magnet generators (PMG) represent the cutting edge technology in modern wind mills. The efficiency remains high (over 90%) at partial loads. To improve the machine efficiency even further, every aspect of machine losses has to be analyzed. Additional losses are often given as a certain percentage without providing any detailed information about the actual calculation process; meanwhile, there are many design-dependent losses that have an effect on the total amount of additional losses and that have to be taken into consideration. Additional losses are most often eddy current losses in different parts of the machine. These losses are usually difficult to calculate in the design process. In this doctoral thesis, some additional losses are identified and modeled. Further, suggestions on how to minimize the losses are given. Iron losses can differ significantly between the measured no-load values and the loss values under load. In addition, with embedded magnet rotors, the quadrature-axis armature reaction adds losses to the stator iron by manipulating the harmonic content of the flux. It was, therefore, re-evaluated that in salient pole machines, to minimize the losses and the loss difference between the no-load and load operation, the flux density has to be kept below 1.5 T in the stator yoke, which is the traditional guideline for machine designers. Eddy current losses may occur in the end-winding area and in the support structure of the machine, that is, in the finger plate and the clamping ring. With construction steel, these losses account for 0.08% of the input power of the machine. These losses can be reduced almost to zero by using nonmagnetic stainless steel. In addition, the machine housing may be subjected to eddy current losses if the flux density exceeds 1.5 T in the stator yoke. Winding losses can rise rapidly when high frequencies and 10–15 mm high conductors are used. In general, minimizing the winding losses is simple. For example, it can be done by dividing the conductor into transposed subconductors. However, this comes with the expense of an increase in the DC resistance. In the doctoral thesis, a new method is presented to minimize the winding losses by applying a litz wire with noninsulated strands. The construction is the same as in a normal litz wire but the insulation between the subconductors has been left out. The idea is that the connection is kept weak to prevent harmful eddy currents from flowing. Moreover, the analytical solution for calculating the AC resistance factor of the litz-wire is supplemented by including an end-winding resistance in the analytical solution. A simple measurement device is developed to measure the AC resistance in the windings. In the case of a litz-wire with originally noninsulated strands, vacuum pressure impregnation (VPI) is used to insulate the subconductors. In one of the two cases studied, the VPI affected the AC resistance factor, but in the other case, it did not have any effect. However, more research is needed to determine the effect of the VPI on litz-wire with noninsulated strands. An empirical model is developed to calculate the AC resistance factor of a single-layer formwound winding. The model includes the end-winding length and the number of strands and turns. The end winding includes the circulating current (eddy currents that are traveling through the whole winding between parallel strands) and the main current. The end-winding length also affects the total AC resistance factor.

Wind Turbine Direct-Drive Permanent-Magnet Generator with Direct Liquid Cooling for Mass Reduction

Today’s electrical machine technology allows increasing the wind turbine output power by an order of magnitude from the technology that existed only ten years ago. However, it is sometimes argued that high-power direct-drive wind turbine generators will prove to be of limited practical importance because of their relatively large size and weight. The limited space for the generator in a wind turbine application together with the growing use of wind energy pose a challenge for the design engineers who are trying to increase torque without making the generator larger. When it comes to high torque density, the limiting factor in every electrical machine is heat, and if the electrical machine parts exceed their maximum allowable continuous operating temperature, even for a short time, they can suffer permanent damage. Therefore, highly efficient thermal design or cooling methods is needed. One of the promising solutions to enhance heat transfer performances of high-power, low-speed electrical machines is the direct cooling of the windings. This doctoral dissertation proposes a rotor-surface-magnet synchronous generator with a fractional slot nonoverlapping stator winding made of hollow conductors, through which liquid coolant can be passed directly during the application of current in order to increase the convective heat transfer capabilities and reduce the generator mass. This doctoral dissertation focuses on the electromagnetic design of a liquid-cooled direct-drive permanent-magnet synchronous generator (LC DD-PMSG) for a directdrive wind turbine application. The analytical calculation of the magnetic field distribution is carried out with the ambition of fast and accurate predicting of the main dimensions of the machine and especially the thickness of the permanent magnets; the generator electromagnetic parameters as well as the design optimization. The focus is on the generator design with a fractional slot non-overlapping winding placed into open stator slots. This is an a priori selection to guarantee easy manufacturing of the LC winding. A thermal analysis of the LC DD-PMSG based on a lumped parameter thermal model takes place with the ambition of evaluating the generator thermal performance. The thermal model was adapted to take into account the uneven copper loss distribution resulting from the skin effect as well as the effect of temperature on the copper winding resistance and the thermophysical properties of the coolant. The developed lumpedparameter thermal model and the analytical calculation of the magnetic field distribution can both be integrated with the presented algorithm to optimize an LC DD-PMSG design. Based on an instrumented small prototype with liquid-cooled tooth-coils, the following targets have been achieved: experimental determination of the performance of the direct liquid cooling of the stator winding and validating the temperatures predicted by an analytical thermal model; proving the feasibility of manufacturing the liquid-cooled tooth-coil winding; moreover, demonstration of the objectives of the project to potential customers.

Hiilinanojohteiden makroskooppinen johtavuus

Hiilinanojohteet ovat sähkönjohteita, joiden valmistuksessa on käytetty hiilinanoputkia, eli yhden atomikerroksen paksuisesta hiiliatomiverkosta koostuvia rakenteita. Hiilinanoputket ovat viime vuosina keränneet suurta mielenkiintoa erinomaisten fysikaalisten ominaisuuksiensa ansiosta. Tämän työn tavoitteena on selvittää, voitaisiinko hiilinanojohteiden sähkönjohtavuus saada riittävälle tasolle, jotta niillä saatettaisiin korvata nykyisiä kuparista valmistettuja johteita. Vaikka kuparilla on erinomainen johtavuus, sen käytöllä on omat heikkoutensa, kuten korkea hinta, virran ahtautuminen, suuri tiheys ja heikko mekaaninen kestävyys. Hiilinanojohteet voisivat olla yksi osa-alue kehitettäessä uusia energiatehokkaita ja ympäristöystävällisiä laitteita nyky-yhteiskunnan tarpeisiin. Työn tulosten perusteella voidaan todeta, että nykyisten hiilinanojohteiden sähkönjohtavuus on yhä liian pieni laajamittaiseen käyttöön. Johtavuus on kuitenkin lisääntynyt jatkuvasti viime vuosina. Kehitystyön avulla hiilimateriaalin potentiaalia saadaan hyödynnettyä koko ajan enemmän, ja ajan myötä hiilijohteista voi tulla varteenotettava kilpailija perinteisille johdemateriaaleille. Hiilinanojohteet tulevat luultavasti aluksi yleistymään käyttökohteissa, joissa niiden muut ominaisuudet täydentävät hyvin sähkönjohtavuutta.

Piirilevyn suunnittelu suurelle virralle DC/DC-muuntimeen

Ajoneuvoissa, kuten busseissa, käytetään yleensä 24 VDC järjestelmiä ja tämä ei muutu myöskään sähköajoneuvojen kohdalla. Sähköajoneuvoissakin tarvitaan siis 24 VDC matalajänniteakustoja valoille, pyyhkijöille ja muille matalan jännitteen järjestelmille. Lisäksi sähköajoneuvoissa on esimerkiksi ilmastointi ja paineilmankompressori, jotka tarvitsevat taajuusmuuttajan pyörittämään niitä. Tässä työssä suunnitellaan suuren virran piilevy DC/DC-muuntimeen, joka on osa ajoneuvokäyttöön suunnitellun invertterin ja DC/DC-muuntimen yhdistelmälaitetta. Työn pääpaino on piirilevyn suunnittelussa, mutta työssä kerrotaan lyhyesti koko laitteen kytkentä ja käyttötarkoitus. Työssä kerrotaan myös tehopiirilevylle tulevien komponenttien valinta, mitoitus ja jäähdytys. Käydään läpi suuren virran piirilevysuunnittelun mitoitusperiaatteet ja mitä seikkoja siinä erityisesti tulee ottaa huomioon. Lisäksi käsitellään piirilevyn liityntöjä ja virtakiskojen lämpenemää virranahtautumisen takia. Suunniteltua piirilevyä mitataan ja sen toimintaa kokeillaan prototyyppilaitteessa. Protoyyppilaitteella havaitaan virtakiskojen lämpenevän liikaa ja huomataan ongelma kytkenssä. Kytkentää korjattiin ja toimintaa analysoitiin uudestaan, jonka jälkeen havaittiin piirilevyn lämpenemän tippuneen 20 °C. Lopputuloksena piirilevyn lämpenemä, korjatulla kytkennällä, on suunnitellun mukainen. Lopussa esitetään piirilevyn korvaamista moduuliratkaisulla laitteen parantamiseksi sarjatuotantoon.

A Comaparison Study of EM and Physical Equivalent Circuit Modeling for MIM CMOS Capacitors

In this Letter a new physical model for metal-insulatormetal CMOS capacitors is presented. In the model the parameters of the circuit are derived from the physical structural details. Physical behaviors due to metal skin effect and inductance have been considered. The model has been confirmed by 3D EM simulator and design rules proposed. The model presented is scalable with capacitor geometry, allowing designers to predict and optimize quality factor. The approach has been verified for MIM CMOS capacitors

A new procedure to derive transmission-line parameters: Applications and restrictions

The objective of this paper is to show an alternative methodology to calculate transmission-line parameters per unit length. With this methodology, the transmission-line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency-dependent transmission-line parameters by using Carson's and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency-dependent transmission-line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a two-phase and a three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulations results for a typical frequency spectrum of switching transients (10 Hz to 10 kHz).